As per your first question, its been show that exercise in general is beneficial for various health aspects (like increased immune system function) however, very strenous exercise on a continuous basis can divert ''energy'' from immune fonction toward anabolism/system repair. Therefore, I imagine that going for light exercise would be your best option .
For you second question, you might try Spike (its caffeine content is basically negligible). The reason you can't take caffeine/theophylline is simply that most of the antibiotics used to treat bacterial prostatitis increase caffeine toxicity (either from the effect side or actual cellular damage or both). Considering that most people don't listen to their doctors, people who have take these kinds of medication would have fallen left and right. Its probably a case of better safe than sorry.
Hang in there, the treatment for acute and chronic bacterial prostatitis ranges from 4 to 6 weeks (acute) to 4 to 12 weeks (chronic) depending on the antibiotics used.
Yep, life sure does suck.